Table 1.

List of definitions of all the parameters.

Variable/parameter	Definition
$f_s$	Lateral frictional force
$f_t$	Penetration resistance force
$f_s+f_t$	Resultant force of penetration and friction
$f_g$	Growing force of the root
$E_s$	Elastic coefficient associated with $f_s$
$E_t$	Elastic coefficient associated with $f_t$
$\phi$	Wall extensibility
$u_c$	Threshold of displacement for root to slip
$u_{\mathit{lift}}$	Threshold of displacement for root to lift up
$\delta u$	Strain associated with the unit time scale
$t_{\mathit{lift}}$	Time for root to lift up
$u(+)$	Virtual displacement of the root base
$u(-)$	Virtual displacement of the root tip
$G_p$	Primary growth rate of the root
$G_s$	Secondary growth rate of the root
$L(t)$	Length of the zone presenting root hairs
$L_0$	Initial length of the zone presenting root hairs
$t$	Time variable
$u(\pm )$	Virtual displacement $\mathrm{u}(+)$ or $\mathrm{u}(-)$
$R(t)$	Radius of the root
$R_0$	Initial radius of the root
$u_s$	Effective displacement of the frictional domain
$P_0$	Initial earth pressure
$P_p$	Preconsolidation stress
$P^{\prime }(=P_p-P_0)$	Relative soil pressure
$P_t$	Current soil pressure
$e_0$	Initial void ratio
$e_t$	Current void ratio
$\mathrm{\lambda }$	Normal consolidation coefficient
$V_0$	Initial void volume
$V_t$	Current void volume
$V_s$	Soil volume
$D_v$	Distance from the depth at which the soil does not move when the root grows
$S$	Soil mechanical parameter
$\alpha$	Non-dimensional parameter representing growth anisotropy of the root
$\beta$	Non-dimensional parameter representing ratio between $P_p$ and $E_s$
$\gamma$	Non-dimensional parameter representing ratio between $S$ and $G_s$
$E$	Young’s modulus of the soil